Strong vs Weak Operator Topology

Let $H$ be a Hilbert space and $B(H)$ its bounded linear operators. A net $(T_i)$ in $B(H)$ converges to $T\in B(H)$:

• in the strong operator topology (SOT) if $\lVert T_i x-Tx\rVert\to0$ for every $x\in H$;
• in the weak operator topology (WOT) if $\langle T_i x,y\rangle\to\langle Tx,y\rangle$ for every $x,y\in H$.